1/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/12

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1/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/121/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/121/(x-1)x+1/x(x+1)+…+1/

1/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/12
1/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/12

1/(x-1)x+1/x(x+1)+…+1/(x+9)(x+10)=11/12
1/(x-1)x可以拆开成1/(x-1)-1/x.类似地可以依次拆开后面的每一项,前后项相互抵消,得1/(x-1)-1/(x+10)=11/12,通分,得11/(x-1)(x+10)=11/12即(x-1)(x+10)=12,解得x=-11或x=2